By definition, a prediction describes a declaration made in advance of an event.Therefore we cannot predict the past.

If you are looking for a verb, then I have tried to answer your question here:I think people often use the word predict when talking about the past, so this can be confusing. For example, someone might say "I predict that X (an event in the past) caused Y (an effect noticed in the present)". It might be more suitable to replace the verb 'predict' with the verb 'guess' or 'suppose' or 'suspect'.E.g. "I suspect that X caused Y." Or "I suspect that gravity caused that apple on the ground to fall from its tree."

but you are missing the point. what happens when you do not know what happened in the past? can it be considered then a prediction? anyway, my main question is that, is there a word that could describe a prediction made for the future and the past?